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# Fourth power of 2^(root(2) is:

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Intern
Joined: 19 May 2014
Posts: 31
Fourth power of 2^(root(2) is: [#permalink]

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22 May 2014, 04:18
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Difficulty:

35% (medium)

Question Stats:

54% (00:46) correct 46% (00:31) wrong based on 166 sessions

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Fourth power of $$2^{\sqrt{2}$$ is:

(A) 4
(B) $$16^{\sqrt{2}$$
(C) 16
(D) 64
(E) 256

Source: Original Question
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 May 2014, 04:23, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 43862
Re: Fourth power of 2^(root(2) is: [#permalink]

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22 May 2014, 04:30
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MavenQ wrote:
Fourth power of $$2^{\sqrt{2}$$ is:

(A) 4
(B) $$16^{\sqrt{2}$$
(C) 16
(D) 64
(E) 256

Source: Original Question

$$(a^m)^n=a^{mn}$$

$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$ (if exponentiation is indicated by stacked symbols, the rule is to work from the top down)

Thus, $$(2^{\sqrt{2}})^4=2^{4\sqrt{2}}=16^{\sqrt{2}}$$.

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: Fourth power of 2^(root(2) is: [#permalink]

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22 May 2014, 20:47

$${a^b}^{c} = a^{(b^c)}$$

$$(a^b)^c = a^{bc}$$

For example:

$${2^3}^{2}= 2^9 = 512$$

$$(2^3)^2 = 2^6 = 64 Or$$

$$(2^3)^2 = 8^2 = 64$$
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Re: Fourth power of 2^(root(2) is: [#permalink]

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24 Apr 2016, 14:49
Hello from the GMAT Club BumpBot!

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Re: Fourth power of 2^(root(2) is: [#permalink]

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28 Sep 2017, 23:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Fourth power of 2^(root(2) is:   [#permalink] 28 Sep 2017, 23:07
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